As the harvesting of fish through commercial fisheries becomes both harder and less economically viable, the world is becoming increasingly dependent on aquaculture to provide fish for human consumption. The closely related activity of stock enhancement, whereby large numbers of fish are reared and then released, is a common practice aimed at increasing the numbers of fish in rivers and along coasts. Aquaculture and stock enhancement practices raise a number of welfare and conservation issues both for fish that are reared within captivity, and for the local populations and habitats that are influenced by fish-rearing activities. In this review, we illustrate how fish farms and hatcheries have directly affected fish welfare. Examples cover on-farm fish husbandry and healthcare, the interactions between farmed and wild fish, and survival of fish released for stock enhancement. These aspects are often intertwined with important conservation issues. Thus, we also review direct effects that aquaculture-generated pollution can have on local habitats, issues associated with feeding reared fish, and problems created by alien fish (either escapees or intentionally released fish). While awareness of fish welfare is certainly growing, so is the rate at which fish are reared. There is, therefore, a pressing need to understand the welfare and conservation issues that are affected by aquaculture and stock enhancement.